Valence shell correlation

Table 5. Valence shell correlation energy in H2O1) given by MB-RSPT treatment116) and the INO-CI calculations96) including all singly and doubly excited configurations (Cl-SD)...

The valence shell correlation energies in Tables I and II were based on a frozen ls-3p UHF core. Additional calculations with only a Is or ls-2p UHF core indicate that correlation energy differences for different d-electronic configurations can change typically by < 0.1 eV when correlation of the 3s/3p shell is included in the MP model. While these changes are rather small, they can correspond to appreciable relative changes (typically 10-20%). So as to eliminate this source of uncertainty, we have employed a frozen ls-2p core for... 

Table I. Valence Shell Correlation Energy (eV) for the 3d / D States of Cr and Co " " ...

Table II. Valence Shell Correlation Energy for Co " " and Co Ions...

MH2 j which permits the valence-shell correlation energy to be picked... 

Valence shell correlation energy E/E,) in HpO given by MB-RSPT... 

The entries in Tables 4.6 and 4,7 are only valence shell correlation energies but no restriction was imposed upon the number of used unoccupied orbitals given by the particular basis set. From Tables 4.5... 

This was recognized by Mof tt and led to his theory of atoms in molecules . However, he tried to obtain even the valence shell correlations from free atoms. Since valence electrons in a molecule do not preserve their atomic character, the idea of empirical intra-atomic correlation corrections applies properly only to inner shells (see also Section XXV). 

Calculations of atomic quadrupole moments are still of interest, particularly for heavier atoms where relativistic accuracy is required. Sundholm102 has reported a finite-element MCSCF method to calculate the quadrupole of Ar+ and finds a final value of —0.5271 au in comparison with a recent experimental determination of —0.5208 au. The Hartree-Fock value is —0.57213 au and the valence shell correlation correction, amounting to 0.04844 au, accounts for most of the additional contribution, a result which may be of some significance for molecular calculations involving atoms in the intermediate range of atomic numbers. 

In the case of the basis applied one can estimate the valence-shell correlation, which is in its calculation about 70-75%. [The total energy per unit cell at the MP2 level is — 77.168 a.u., at the HF level —76.893 and their difference is 7.5 eV.55 On the other hand the valence shell-correlation energy of an acetylene unit was estimated to be 10 eV56]. Extrapolation to 100% correlation has given a gap of 2.5 eV.M... 

An individual interpair (or interbond) correlation energy srs increases considerably in absolute value on going from LiH to CH4. The reason is that the bond angle decreases steadily from LiH to CH4 and so the electrons in the different bonds come increasingly closer to each other. The closer two pairs are, the stronger is their interpair correlation interaction. Since the number of interpair terms increase (compared to the number of pairs) in the same series, one finds a substantial increase of the interpair contribution to the total valence-shell correlation energy on going from LiH (0%) to CH4 (almost 50%). 

One would like to know, of course, the percent of the full valence-shell correlation energy included in Ei with the best spd basis used. One can obtain an approximate answer to this question if we recall that the valence-shell correlation energy of an acetylene unit was estimated to be about — 10 eV therefore our best energy ( 7.5 eV) should cover 70 to 75% of the total value. Nearly the same result was also obtained recently for an infinite atomic-hydrogen model chain (see Table 5.2). 

In this way hf/n = 392.036284 H was obtained for the infinite polymer. The valence-shell correlation energy per monomer is — 0.663012 H ( 18.5 mH per valence electron), which from previous experience indicates that about half of the estimated full correlation energy can be achieved with the given method and basis set. ... 

Finally, Table 5.7 presents STO-3G and valence split 4-3IG basis correlation calculation results for the four nucleotide bases. The results to be expected in the case of the 4-3 IG basis were estimated by multiplying the corresponding numbers by factors E IE obtained for cytosine in the different methods. If one uses the valence split 4-3 IG basis or estimates the results, it is seen that the correlation eneigy per valence electron provides about 50% of the valence shell correlation using the CCD method with LOs. (One usually estimates the total correlation energy as 1 eV/electron, although this value may actually be too high in the case of valence electrons.)... 

Only for systems with easily polarizable cores, such as those containing the alkali and alkaline-earth atoms, are core correlation effects routinely included because of their sizable effect. This necessity was first demonstrated in the classic study on the first and second row hydrides by Meyer and Rosmus, where they showed that the core-valence electron correlation terms could affect the bond length as strongly as the valence shell correlation, but that the core effect decreased... 

Since even the applied best wave function contains only 75% of the total valence shell correlation, it is interesting to extrapolate the obtained value of Aej(QP) to the case of full correlation. Suhai did this and obtained a gap value of about 241.21 kJ mol" for 100% correlation energy, showing that the estimated theoretical value of Afj(QP) would lie at about 48.24 kJ mol" higher than the estimated experimental gap of 192.96 kJ mol". 3... 

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